Adrian Bejan proposed the constructal law, stating: “For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it”. Such a law can be said to underpin the formation of many systems both animate and inanimate, including, but not limited to, the branching nature of lightning, rivers, lungs and trees.
Various studies based on the constructal law have focused on ‘volume to point’ (VP) flow systems: thermal conduction of heat (A. Bejan, “Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume”, International Journal of Heat and Mass Transfer, Vol. 40, No. 4, pp. 799-816, 1997), liquid flow in a porous media (M. R. Errera et al., “Deterministic Tree Networks for River Drainage Basin”, Fractals, Vol. 6, No. 3, pp. 245-261, 1998), and air flow in lungs (A. H. Reis et al., “Constructal theory of flow architecture of the lungs”, Medical Physics Vol 31 No. 5, pp. 1135-1140, 2004).
Boichot et al described in “Tree-network structure generation for heat conduction by cellular automaton”, Energy Conversion and Management, Vol. 50 no. 2, pp. 376-386, 2009, an approach to the thermal conduction VP problem where a domain was discretized into cellular automota elements. The cellular automota elements were allowed to change between high and low thermal conductivity based on a certain thermal condition during an iterative process. A dendritic branched high conductivity material topology was seen to emerge as the process converged.
Marck et al described in “Evolutionary structural optimization by extension to cool a finite-size volume generating heat”, 2011, 7th International Conference on Computational Heat and Mass Transfer, No. 152, Istanbul (Turkey), an Evolutionary Structural Optimisation approach to the VP problem. The high conductivity topology, made up of abutting automota, evolved via addition during an iterative process based on multiple objective functions. More recent work described by Marck et al in “conductive and convective heat transfers”, OPT-i 2014, International Conference on Engineering and Applied Sciences Optimization, Kos Island (Greece), has started to consider convective effects as well.
Established heat sink manufacturing processes such as extrusion and casting impose constraints on the methods used to design heat sinks These constraints limit both allowable geometry topologies and absolute sizes. The advent of 3D printing (additive manufacture) may remove many of these constraints, enabling practical applications of the constructal law to heat sink design. Heat sinks growing through an additive design process may exhibit a superior thermal performance.